document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=78472>Question 78472</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The figure shows the graph of the polynomial function y=f(x). For which of th values k=0,1,2,or 3 will the equation f(x) = k have complex roots?<BR>\n" );
document.write( "a. 0 <BR>\n" );
document.write( "b. 1<BR>\n" );
document.write( "c. 2<BR>\n" );
document.write( "d. 3<BR>\n" );
document.write( "I am not sure how to draw the graph to show what it looks like so I will try to explain it. The line comes up from the bottom of quadrant 3 and it goes to the right of (-1,-1)and continues up to (0,2)it then curves down thru (1,0)to (2,-2)and then curves up to just left of (3,0)and keeps going upward. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #56277 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=56277\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> It sounds like you are describing a cubic ( a function with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3 ALIGN=MIDDLE  ALT=\"x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > in it). Since I cannot see the graph, simply look at the graph and see if it intersects with these lines:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0 ALIGN=MIDDLE  ALT=\"y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1 ALIGN=MIDDLE  ALT=\"y=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2 ALIGN=MIDDLE  ALT=\"y=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3 ALIGN=MIDDLE  ALT=\"y=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If it intersects in 3 places it will have 3 real roots. If it intersects at 1 place, then it will have 1 real root and 2 complex root. So if the graph intersects with say <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1 ALIGN=MIDDLE  ALT=\"y=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > at one spot, then it will have 2 complex roots. </SPAN>\n" );
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